For unital simple Z-stable C*-algebras, every non-compact Cuntz class is contractible, yielding the homotopy groups of all Cuntz classes.
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Contractible Cuntz classes in $Z$-stable C$^*$-algebras
For unital simple Z-stable C*-algebras, every non-compact Cuntz class is contractible, yielding the homotopy groups of all Cuntz classes.